Abstract
On a compact surface endowed with any Spinc structure, we give a formula involving the Energy-Momentum tensor in terms of geometric quantities. A new proof of a Bär-type inequality for the eigenvalues of the Dirac operator is given. The round sphere 𝕊2 with its canonical Spinc structure satisfies the limiting case. Finally, we give a spinorial characterization of immersed surfaces in 𝕊2 × ℝ by solutions of the generalized Killing spinor equation associated with the induced Spinc structure on 𝕊2 × ℝ.
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